The asymptotic distributions of the number of vertices of a given degree in random graphs, where the probabilities of edges may not be the same, are given. Using the method of Poisson convergence, distributions in a general and particular cases (complete, almost regular and bipartite graphs) are obtained.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1031, author = {Wojciech Kordecki}, title = {Poisson convergence of numbers of vertices of a given degree in random graphs}, journal = {Discussiones Mathematicae Graph Theory}, volume = {16}, year = {1996}, pages = {157-172}, zbl = {0877.05053}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1031} }
Wojciech Kordecki. Poisson convergence of numbers of vertices of a given degree in random graphs. Discussiones Mathematicae Graph Theory, Tome 16 (1996) pp. 157-172. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1031/
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